一类求解全局优化问题的单参数填充函数算法  

Single Parameter Filled Function Algorithm for Global Optimization

作　　者：段晓辉 景书杰[1] 牛海峰[1] Duan Xiaohui;Jing Shujie;Niu Haifeng(School of Mathematics and Information Science,Henan Polytechnical University,Jiaozuo 454000,China)

机构地区：[1]河南理工大学数学与信息科学学院,河南焦作454000

出　　处：《洛阳师范学院学报》2022年第8期13-16,共4页Journal of Luoyang Normal University

基　　金：国家自然科学基金资助项目(U1504104)。

摘　　要：全局优化算法是最优化算法出现后众多优化工作者和优化应用问题所追求的算法,但是除了线性规划和凸规划以外,其他优化问题的全局优化算法难度较大.目前填充函数算法是用来求解非线性全局优化问题的一类有效且可行的方法,但已有的填充函数由于存在指数项和较多参数而导致数值实验效果不理想.本文在无不等式约束条件下,提出了一个满足填充函数定义且连续可微的单参数填充函数,分析讨论了该函数的性质,并设计了相应的填充函数算法.最后结合多峰值函数进行了数值实验,数值结果证明提出的填充函数及算法是有效可行的.Since the emergence of optimization algorithm,global optimization algorithm is a method pursued by many optimization workers in optimizing application problems.However,in addition to linear programming and convex programming,global optimization algorithms for other optimization problems have always been difficult.At present,the filled function algorithm is an effective and feasible approach to solve the nonlinear global optimization problems.Existing filled functions have unsatisfactory results due to the exponential term and many parameters.Under no inequality constraint,this paper proposes a continuously differentiable single parameter filled function that satisfies the definition of the filled function.The properties of the function are analyzed and discussed,and the corresponding filled function algorithm is designed.Finally,numerical experiments are carried out in combination with multi-peak functions,and the numerical results prove that the proposed filled function and algorithm are effective and feasible.

关 键 词：全局优化 填充函数 多峰值函数 非线性全局优化 

分 类 号：O224[理学—运筹学与控制论]